Nucleation, Growth, and Bundling of GaN Nanowires in Molecular Beam Epitaxy: Disentangling the Origin of Nanowire Coalescence

Abstract

We investigate the nucleation, growth, and coalescence of spontaneously formed GaN nanowires in molecular beam epitaxy combining the statistical analysis of scanning electron micrographs with Monte Carlo growth models. We find that (i) the nanowire density is limited by the shadowing of the substrate from the impinging fluxes by already existing nanowires, (ii) shortly after the nucleation stage, nanowire radial growth becomes negligible, and (iii) coalescence is caused by bundling of nanowires. The latter phenomenon is driven by the gain of surface energy at the expense of the elastic energy of bending and becomes energetically favorable once the nanowires exceed a certain critical length.

Elastic versus Plastic Strain Relaxation in Coalesced GaN Nanowires: An X-Ray Diffraction Study

“…However, the fraction of the surface area covered by the nanowires remains unchanged, which rules out radial growth of nanowires as the origin of coalescence. Instead, we have found that the nanowires bundle together after reaching a certain critical height to reduce the surface energy of their side facets at the expense of the elastic energy due to their bending [18].…”

“…For an estimate, consider two hexagonal nanowires with side facet width a = 10 nm at a distance l = 30 nm between their side facets. The distance between the nanowire centers is then l + 2a = 50 nm, which corresponds to the mean distance between nanowires for a density of 4×10 10 cm −2 , the typical density of nucleated nanowires before the bundling starts [18]. The critical height given by Eq.…”

“…1(a). The following calculation is based on our previous study [18] and serves as a reference for the analysis of plastic deformation at the joints in the next section.…”

“…However, the bending energy of nanowire bundles staying on several pillars can only be evaluated numerically. In our previous work [18], we have approximated this situation by replacing the bundled pair by a single cylindrical nanowire with a volume and cross-sectional area equal to the respective sums of the constituents.…”

“…On the other hand, GaN nanowires coalesce during growth because of their proximity [17]. Recently, we have identified the origin of this coalescence in GaN nanowire ensembles [18]. Dense ensembles of GaN nanowires evolve during growth to ensembles of nanowires with smaller densities and larger diameters.…”